Vortrag
RAAGs and Stable Commutator Length
Vortrag von Dr. Nicolaus Heuer
Datum: 30.05.18 Zeit: 15.45 - 18.00 Raum: ETH HG G 43
Stable commutator length (scl) is a well established invariant of group elements g (write scl(g)) and has both geometric and algebraic meaning. Many classes of "non-positively curved" groups have a gap in stable commutator length: This is, for every non-trivial element g, scl(g) > C for some C > 0. This gap may be thought of as an algebraic injectivity radius and may be found in hyperbolic groups, Baumslag-solitair groups, free products, Mapping class groups, etc. However, the exact size of this gap usually unknown, which is due to a lack of a good source of “quasimorphisms”. In this talk I will construct a new source of quasimorphisms which yield optimal gaps and show that for Right-Angled Artin Groups and their subgroups the gap of stable commutator length is exactly 1/2. I will also show this gap for certain amalgamated free products.